Return-path: Envelope-to: jbovlaste-admin@lojban.org Delivery-date: Wed, 26 Oct 2022 22:44:11 -0700 Received: from [192.168.123.254] (port=48494 helo=jiten.lojban.org) by d7893716a6e6 with smtp (Exim 4.94.2) (envelope-from ) id 1onvgW-007Ey6-L4 for jbovlaste-admin@lojban.org; Wed, 26 Oct 2022 22:44:11 -0700 Received: by jiten.lojban.org (sSMTP sendmail emulation); Thu, 27 Oct 2022 05:44:08 +0000 From: "Apache" To: curtis289@att.net Reply-To: webmaster@lojban.org Subject: [jvsw] Definition Edited At Word pau'au -- By krtisfranks Date: Thu, 27 Oct 2022 05:44:08 +0000 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Message-Id: X-Spam-Score: -2.9 (--) X-Spam_score: -2.9 X-Spam_score_int: -28 X-Spam_bar: -- In jbovlaste, the user krtisfranks has edited a definition of "pau'au" in the language "English". Differences: 2,2c2,2 < ternary mekso operator: p-adic valuation; outputs (positive) infinity if $x_1 = 0$ and, else, outputs sup$($Set($k: k$ is a nonnegative integer, and $(x_2 * (1 - x_3) + p_{x_2} * x_3)^k$ divides $x_1))$, where $p_n$ is the $n$th prime (such that $p_1 = 2$). --- > ternary mekso operator: p-adic valuation; outputs (positive) infinity if $x_1 = 0$ and, else, outputs sup$($Set($k: k$ is a nonnegative integer, and $((1 - x_3)x_2 + x_3 p_{x_2})^k$ divides $x_1))$, where $p_n$ is the $n$th prime (such that $p_1 = 2$). 5,5c5,5 < The terbri order here was defined in analogy to "{de'o}". Normally, $x_1$ should be a rational number, and $x_2$ should be a positive integer; some generalizations may be possible, though. $x_3$ is either $0$ xor $1$, and indicates/toggles between modes: $x_3 = 0$ yields the $x_2$-adic valuation (even for nonprime $x_2$); $x_3 = 1$ yields the $p_{x_2}$-adic valuation. $x_2 = 1, x_3 = 0$ yields positive infinity for any $x_1$ which is within the domain. If $x_1 = n/m$ and is a rational noninteger number such that gcd$(n,m) = 1$, then pau'au$(x_1, x_2, x_3) =$ pau'au$(n, x_2, x_3) -$ pau'au$(m, x_2, x_3)$. --- > The terbri order here was defined in analogy to "{de'o}". Normally, $x_1$ should be a rational number, and $x_2$ should be a positive integer; some generalizations may be possible, though. $x_3$ is either $0$ xor $1$, and indicates/toggles between modes: $x_3 = 0$ yields the $x_2$-adic valuation (even for nonprime $x_2$); $x_3 = 1$ yields the $p_{x_2}$-adic valuation. $x_2 = 1, x_3 = 0$ yields positive infinity for any $x_1$ which is within the domain. If $x_1 = n/m$ and is a rational noninteger number such that gcd$(n,m) = 1$, then pau'au$(x_1, x_2, x_3) =$ pau'au$(n, x_2, x_3) -$ pau'au$(m, x_2, x_3)$. See also: "{fei'i}", "{pi'ei'oi}". This word is often equivalent to or closely related to "{pei'e'a}" (which is, in some ways, more general but less flexible with respect to its input). 13a14,14 \n> Word: integer exponent, In Sense: Old Data: Definition: ternary mekso operator: p-adic valuation; outputs (positive) infinity if $x_1 = 0$ and, else, outputs sup$($Set($k: k$ is a nonnegative integer, and $(x_2 * (1 - x_3) + p_{x_2} * x_3)^k$ divides $x_1))$, where $p_n$ is the $n$th prime (such that $p_1 = 2$). Notes: The terbri order here was defined in analogy to "{de'o}". Normally, $x_1$ should be a rational number, and $x_2$ should be a positive integer; some generalizations may be possible, though. $x_3$ is either $0$ xor $1$, and indicates/toggles between modes: $x_3 = 0$ yields the $x_2$-adic valuation (even for nonprime $x_2$); $x_3 = 1$ yields the $p_{x_2}$-adic valuation. $x_2 = 1, x_3 = 0$ yields positive infinity for any $x_1$ which is within the domain. If $x_1 = n/m$ and is a rational noninteger number such that gcd$(n,m) = 1$, then pau'au$(x_1, x_2, x_3) =$ pau'au$(n, x_2, x_3) -$ pau'au$(m, x_2, x_3)$. Jargon: Gloss Keywords: Word: p-adic order, In Sense: Word: p-adic valuation, In Sense: Word: prime-logarithm, In Sense: Place Keywords: New Data: Definition: ternary mekso operator: p-adic valuation; outputs (positive) infinity if $x_1 = 0$ and, else, outputs sup$($Set($k: k$ is a nonnegative integer, and $((1 - x_3)x_2 + x_3 p_{x_2})^k$ divides $x_1))$, where $p_n$ is the $n$th prime (such that $p_1 = 2$). Notes: The terbri order here was defined in analogy to "{de'o}". Normally, $x_1$ should be a rational number, and $x_2$ should be a positive integer; some generalizations may be possible, though. $x_3$ is either $0$ xor $1$, and indicates/toggles between modes: $x_3 = 0$ yields the $x_2$-adic valuation (even for nonprime $x_2$); $x_3 = 1$ yields the $p_{x_2}$-adic valuation. $x_2 = 1, x_3 = 0$ yields positive infinity for any $x_1$ which is within the domain. If $x_1 = n/m$ and is a rational noninteger number such that gcd$(n,m) = 1$, then pau'au$(x_1, x_2, x_3) =$ pau'au$(n, x_2, x_3) -$ pau'au$(m, x_2, x_3)$. See also: "{fei'i}", "{pi'ei'oi}". This word is often equivalent to or closely related to "{pei'e'a}" (which is, in some ways, more general but less flexible with respect to its input). Jargon: Gloss Keywords: Word: p-adic order, In Sense: Word: p-adic valuation, In Sense: Word: prime-logarithm, In Sense: Word: integer exponent, In Sense: Place Keywords: You can go to to see it.